Given a curved regression, the correlation index is defined by
 |
(1)
|
where 
and 
are the standard deviations of the data points 
and the estimates 
given by the regression line (Kenney and Keeping 1962, p. 293).
Unfortunately, the quantity 
appears not to be defined by Kenney and Keeping (1962,
p. 293). Then
 |  |  |
(2)
|
 |  |  |
(3)
|
where 
is the variance of the observed 
s about the best-fitting curved line (Kenney and Keeping 1962,
p. 293).
